Mathematics: Show that the series is convergent or divergent: i need the b) part so badly

Show that the series is convergent or divergent:

Ответ:

BeautyxQueen

16.01.2022

$\displaystyle\sum_{n\ge0}\frac{2e^n}{e^{2n}+1}=\sum_{n\ge0}\frac2{e^n+\frac1{e^n}}$

As $n\to\infty$ , $\dfrac1{e^n}$ becomes insignificant, so you can compare this series to

$\displaystyle\sum_{n\ge0}\frac2{e^n}$

since

$e^n\dfrac2{e^n+\frac1{e^n}}$

This comparison series converges as it's geometric:

$\displaystyle\sum_{n\ge0}\frac2{e^n}=2\sum_{n\ge0}\left(\frac1e\right)^n=\frac{2e}{e-1}$

Since this convergent series is smaller than the first series, the first series must also be convergent.

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Ответ:

deijiahshatia

09.09.2021

Mathematics

23 pounds is 4 times as heavy as each container. Since 23 is divided by four containers...there is 5.75 pounds of cheese in container. 5.75 multiplied by 4 is 23.

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Show that the series is convergent or divergent:

i need the b) part so badly

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